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Computational Framework for the Finite Element Method in MATLAB® and Python

Author : Pavel Sumets

Publisher : CRC Press

Page : 182 pages

File Size : 20,18 MB

Release : 2022-08-11

Category : Computers

ISBN : 1000609995

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Book Description

Computational Framework for the Finite Element Method in MATLAB® and Python aims to provide a programming framework for coding linear FEM using matrix-based MATLAB® language and Python scripting language. It describes FEM algorithm implementation in the most generic formulation so that it is possible to apply this algorithm to as many application problems as possible. Readers can follow the step-by-step process of developing algorithms with clear explanations of its underlying mathematics and how to put it into MATLAB and Python code. The content is focused on aspects of numerical methods and coding FEM rather than FEM mathematical analysis. However, basic mathematical formulations for numerical techniques which are needed to implement FEM are provided. Particular attention is paid to an efficient programming style using sparse matrices. Features Contains ready-to-use coding recipes allowing fast prototyping and solving of mathematical problems using FEM Suitable for upper-level undergraduates and graduates in applied mathematics, science or engineering Both MATLAB and Python programming codes are provided to give readers more flexibility in the practical framework implementation



Computational Framework for the Finite Element Method in MATLAB® and Python

Author : Pavel Sumets

Publisher : CRC Press

Page : 166 pages

File Size : 49,30 MB

Release : 2022-08-11

Category : Mathematics

ISBN : 1000610020

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Book Description

Computational Framework for the Finite Element Method in MATLAB® and Python aims to provide a programming framework for coding linear FEM using matrix-based MATLAB® language and Python scripting language. It describes FEM algorithm implementation in the most generic formulation so that it is possible to apply this algorithm to as many application problems as possible. Readers can follow the step-by-step process of developing algorithms with clear explanations of its underlying mathematics and how to put it into MATLAB and Python code. The content is focused on aspects of numerical methods and coding FEM rather than FEM mathematical analysis. However, basic mathematical formulations for numerical techniques which are needed to implement FEM are provided. Particular attention is paid to an efficient programming style using sparse matrices. Features Contains ready-to-use coding recipes allowing fast prototyping and solving of mathematical problems using FEM Suitable for upper-level undergraduates and graduates in applied mathematics, science or engineering Both MATLAB and Python programming codes are provided to give readers more flexibility in the practical framework implementation



Automated Solution of Differential Equations by the Finite Element Method

Author : Anders Logg

Publisher : Springer Science & Business Media

Page : 723 pages

File Size : 25,46 MB

Release : 2012-02-24

Category : Computers

ISBN : 3642230997

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Book Description

This book is a tutorial written by researchers and developers behind the FEniCS Project and explores an advanced, expressive approach to the development of mathematical software. The presentation spans mathematical background, software design and the use of FEniCS in applications. Theoretical aspects are complemented with computer code which is available as free/open source software. The book begins with a special introductory tutorial for beginners. Following are chapters in Part I addressing fundamental aspects of the approach to automating the creation of finite element solvers. Chapters in Part II address the design and implementation of the FEnicS software. Chapters in Part III present the application of FEniCS to a wide range of applications, including fluid flow, solid mechanics, electromagnetics and geophysics.



Solving PDEs in Python

Author : Hans Petter Langtangen

Publisher : Springer

Page : 152 pages

File Size : 40,55 MB

Release : 2017-03-21

Category : Computers

ISBN : 3319524623

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Book Description

This book offers a concise and gentle introduction to finite element programming in Python based on the popular FEniCS software library. Using a series of examples, including the Poisson equation, the equations of linear elasticity, the incompressible Navier–Stokes equations, and systems of nonlinear advection–diffusion–reaction equations, it guides readers through the essential steps to quickly solving a PDE in FEniCS, such as how to define a finite variational problem, how to set boundary conditions, how to solve linear and nonlinear systems, and how to visualize solutions and structure finite element Python programs. This book is open access under a CC BY license.





Finite Element Computations in Mechanics with R

Author : Khameel Bayo Mustapha

Publisher : CRC Press

Page : 368 pages

File Size : 26,57 MB

Release : 2018-04-17

Category : Science

ISBN : 1351385593

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Book Description

Finite Element Computations in Mechanics with R: A Problem-Centred Programming Approach provides introductory coverage of the finite element method (FEM) with the R programming language, emphasizing links between theory and implementation of FEM for problems in engineering mechanics. Useful for students, practicing engineers, and researchers, the text presents the R programming as a convenient easy-to-learn tool for analyzing models of mechanical systems, with finite element routines for structural, thermal, and dynamic analyses of mechanical systems, and also visualization of the results. Full-color graphics are used throughout the text.



The Finite Element Method: Theory, Implementation, and Applications

Author : Mats G. Larson

Publisher : Springer Science & Business Media

Page : 403 pages

File Size : 11,74 MB

Release : 2013-01-13

Category : Computers

ISBN : 3642332870

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Book Description

This book gives an introduction to the finite element method as a general computational method for solving partial differential equations approximately. Our approach is mathematical in nature with a strong focus on the underlying mathematical principles, such as approximation properties of piecewise polynomial spaces, and variational formulations of partial differential equations, but with a minimum level of advanced mathematical machinery from functional analysis and partial differential equations. In principle, the material should be accessible to students with only knowledge of calculus of several variables, basic partial differential equations, and linear algebra, as the necessary concepts from more advanced analysis are introduced when needed. Throughout the text we emphasize implementation of the involved algorithms, and have therefore mixed mathematical theory with concrete computer code using the numerical software MATLAB is and its PDE-Toolbox. We have also had the ambition to cover some of the most important applications of finite elements and the basic finite element methods developed for those applications, including diffusion and transport phenomena, solid and fluid mechanics, and also electromagnetics.​



The Finite Volume Method in Computational Fluid Dynamics

Author : F. Moukalled

Publisher : Springer

Page : 799 pages

File Size : 43,60 MB

Release : 2015-08-13

Category : Technology & Engineering

ISBN : 3319168746

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Book Description

This textbook explores both the theoretical foundation of the Finite Volume Method (FVM) and its applications in Computational Fluid Dynamics (CFD). Readers will discover a thorough explanation of the FVM numerics and algorithms used for the simulation of incompressible and compressible fluid flows, along with a detailed examination of the components needed for the development of a collocated unstructured pressure-based CFD solver. Two particular CFD codes are explored. The first is uFVM, a three-dimensional unstructured pressure-based finite volume academic CFD code, implemented within Matlab. The second is OpenFOAM®, an open source framework used in the development of a range of CFD programs for the simulation of industrial scale flow problems. With over 220 figures, numerous examples and more than one hundred exercise on FVM numerics, programming, and applications, this textbook is suitable for use in an introductory course on the FVM, in an advanced course on numerics, and as a reference for CFD programmers and researchers.



Introduction to Finite Elements in Engineering

Author : Tirupathi R. Chandrupatla

Publisher :

Page : 453 pages

File Size : 35,54 MB

Release : 2002-01

Category : Engineering mathematics

ISBN : 9780131784536

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Book Description

CD-ROM includes: complete self-contained computer programs with source codes in Visual Basic, Excel-based Visual Basic, MATLAB, QUICKBASIC, FORTRAN, and C.



Introduction to Radar Using Python and MATLAB

Author : Lee Andrew (Andy) Harrison

Publisher : Artech House

Page : 491 pages

File Size : 21,52 MB

Release : 2019-10-31

Category : Technology & Engineering

ISBN : 1630815993

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Book Description

This comprehensive resource provides readers with the tools necessary to perform analysis of various waveforms for use in radar systems. It provides information about how to produce synthetic aperture (SAR) images by giving a tomographic formulation and implementation for SAR imaging. Tracking filter fundamentals, and each parameter associated with the filter and how each affects tracking performance are also presented. Various radar cross section measurement techniques are covered, along with waveform selection analysis through the study of the ambiguity function for each particular waveform from simple linear frequency modulation (LFM) waveforms to more complicated coded waveforms. The text includes the Python tool suite, which allows the reader to analyze and predict radar performance for various scenarios and applications. Also provided are MATLAB® scripts corresponding to the Python tools. The software includes a user-friendly graphical user interface (GUI) that provides visualizations of the concepts being covered. Users have full access to both the Python and MATLAB source code to modify for their application. With examples using the tool suite are given at the end of each chapter, this text gives readers a clear understanding of how important target scattering is in areas of target detection, target tracking, pulse integration, and target discrimination.